[GMAT math practice question]
If n is the sum of the first 50 positive integers, what is the greatest prime factor of n?
A. 3
B. 5
C. 7
D. 17
E. 51
If n is the sum of the first 50 positive integers, what is t
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- Max@Math Revolution
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n = 1 + 2 + 3 + 4 + ...... + 47 + 48 + 49 + 50Max@Math Revolution wrote: If n is the sum of the first 50 positive integers, what is the greatest prime factor of n?
A. 3
B. 5
C. 7
D. 17
E. 51
Let's add the values in pairs, starting from the outside and work towards the middle
n = (1 + 50) + (2 + 49) + (3 + 48) + . . ..
= 51 + 51 + 51 + .....
Since we are adding 50 values (from 1 to 50), we will get 25 PAIRS of values
So, n = (25)(51)
Factor: n = (5)(5)(3)(17)
Answer: 17
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Alternatively, we can use the following formula:Max@Math Revolution wrote:[GMAT math practice question]
If n is the sum of the first 50 positive integers, what is the greatest prime factor of n?
A. 3
B. 5
C. 7
D. 17
E. 51
Sum of the first k positive integers = (k)(k+1)/2
For example, the sum of the first 10 positive integers = (10)(10 + 1)/2 = 55
So, the sum of the first 50 positive integers = (50)(50 + 1)/2
= (50)(51)/2
= (25)(51)
= (5)(5)(3)(17)
Answer: D
Cheers,
Brent
- Max@Math Revolution
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=>
1 + 2 + 3 + ... + 50 = 50*(50 + 1)/2 = 25*51 = 52*3*17
17 is the greatest prime factor of n.
Therefore, the answer is D.
Answer: D
1 + 2 + 3 + ... + 50 = 50*(50 + 1)/2 = 25*51 = 52*3*17
17 is the greatest prime factor of n.
Therefore, the answer is D.
Answer: D
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Max@Math Revolution wrote:[GMAT math practice question]
If n is the sum of the first 50 positive integers, what is the greatest prime factor of n?
A. 3
B. 5
C. 7
D. 17
E. 51
The average of consecutive positive integers is: (largest plus smallest)/2. Thus, the sum of the first 50 positive integers is:
(50 + 1)/2 x 50 = 51 x 25 = 17 x 3 x 5^2
So the largest prime factor is 17.
Answer: D
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